xref: /freebsd/contrib/arm-optimized-routines/math/aarch64/sve/sv_expf_inline.h (revision f3087bef11543b42e0d69b708f367097a4118d24)
1 /*
2  * SVE helper for single-precision routines which calculate exp(x) and do
3  * not need special-case handling
4  *
5  * Copyright (c) 2023-2025, Arm Limited.
6  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7  */
8 
9 #ifndef MATH_SV_EXPF_INLINE_H
10 #define MATH_SV_EXPF_INLINE_H
11 
12 #include "sv_math.h"
13 #include "test_sig.h"
14 #include "test_defs.h"
15 
16 struct sv_expf_data
17 {
18   float c1, c3, inv_ln2;
19   float ln2_lo, c0, c2, c4;
20   float ln2_hi, shift;
21 };
22 
23 /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
24    compatibility with polynomial helpers. Shift is 1.5*2^17 + 127.  */
25 #define SV_EXPF_DATA                                                          \
26   {                                                                           \
27     /* Coefficients copied from the polynomial in AdvSIMD variant.  */        \
28     .c0 = 0x1.ffffecp-1f, .c1 = 0x1.fffdb6p-2f, .c2 = 0x1.555e66p-3f,         \
29     .c3 = 0x1.573e2ep-5f, .c4 = 0x1.0e4020p-7f, .inv_ln2 = 0x1.715476p+0f,    \
30     .ln2_hi = 0x1.62e4p-1f, .ln2_lo = 0x1.7f7d1cp-20f,                        \
31     .shift = 0x1.803f8p17f,                                                   \
32   }
33 
34 #define C(i) sv_f32 (d->poly[i])
35 
36 static inline svfloat32_t
expf_inline(svfloat32_t x,const svbool_t pg,const struct sv_expf_data * d)37 expf_inline (svfloat32_t x, const svbool_t pg, const struct sv_expf_data *d)
38 {
39   /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
40      x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
41 
42   svfloat32_t lane_consts = svld1rq (svptrue_b32 (), &d->ln2_lo);
43 
44   /* n = round(x/(ln2/N)).  */
45   svfloat32_t z = svmad_x (pg, sv_f32 (d->inv_ln2), x, d->shift);
46   svfloat32_t n = svsub_x (pg, z, d->shift);
47 
48   /* r = x - n*ln2/N.  */
49   svfloat32_t r = svmsb_x (pg, sv_f32 (d->ln2_hi), n, x);
50   r = svmls_lane (r, n, lane_consts, 0);
51 
52   /* scale = 2^(n/N).  */
53   svfloat32_t scale = svexpa (svreinterpret_u32 (z));
54 
55   /* poly(r) = exp(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4 + C4 r^5.  */
56   svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, lane_consts, 2);
57   svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, lane_consts, 3);
58   svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
59   svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
60   svfloat32_t p0 = svmul_lane (r, lane_consts, 1);
61   svfloat32_t poly = svmla_x (pg, p0, r2, p14);
62 
63   return svmla_x (pg, scale, scale, poly);
64 }
65 
66 #endif // MATH_SV_EXPF_INLINE_H
67